Question

The inverse of a matrix $A = \begin{bmatrix} 0 & 2 & 4 \\ 2 & 4 & 2 \\ 3 & 3 & 1 \end{bmatrix}$ is}

• A. $\begin{bmatrix} -1 & \frac{1}{2} & 0 \\ 1 & 0 & 0\\ \frac{2}{3} & -\frac{3}{8} & \frac{1}{8} \end{bmatrix}$
• B. $\begin{bmatrix} -\frac{1}{8} & \frac{5}{8} & -\frac{3}{4} \\ \frac{1}{4} & -\frac{3}{4} & \frac{1}{2} \\ -\frac{3}{8} & \frac{3}{8} & -\frac{1}{4} \end{bmatrix}$
• C. $\begin{bmatrix} \frac{1}{8} & -\frac{5}{8} & \frac{3}{4} \\ -\frac{1}{4} & \frac{3}{4} & -\frac{1}{2} \\ \frac{3}{8} & -\frac{3}{8} & \frac{1}{4} \end{bmatrix}$
• D. $\begin{bmatrix} -1 & 1 & 0 \\ \frac{1}{2} & 0 & 0 \\ 0 & -\frac{3}{8} & \frac{1}{8} \end{bmatrix}$

Hint:

To quickly verify an inverse matrix in a multiple-choice exam, multiply the first row of original matrix $A$ by the first column of the candidate inverse matrix:
\[ \text{Row 1} \cdot \text{Col 1} = [0, 2, 4] \cdot \begin{bmatrix} 1/8 -1/4 3/8 \end{bmatrix} = 0 - \frac{2}{4} + \frac{12}{8} = -\frac{1}{2} + \frac{3}{2} = 1 \]
This quick check confirms that Option C is correct.

Answer 1

The Correct Option is C